<header>
    基本概念与性质
</header>
<p>
    <span class="title">
        定义（趋向正无穷大）
    </span>
    设ƒ为定义在[a,+∞)上的函数，A为定数。若对任给的ε＞0，存在正数M（≥ a），使得当x＞M时有
    <span class="oneline">
        |ƒ(x) - A|＜ε
    </span>
    则称函数ƒ当x趋于+∞时以A为极限，记作
    <span class="oneline">
        <code> ["limt","x→+∞","ƒ(x)"]</code> = A
    </span>
</p>
<p class="warn">
    温馨提示：趋向负无穷大类似的。
</p>
<p>
    <span class="title">
        定义（趋向x<sub>0</sub>）
    </span>
    设函数ƒ在点x<sub>0</sub>的某个空心领域U<sup>o</sup>(x<sub>0</sub>;δ<sup>'</sup>)内有定义，A为定数。若对任给的ε＞0，存在正数δ（＜δ<sup>'</sup>），使得当0＜|x-x<sub>0</sub>|＜δ时有
    <span class="oneline">
        |ƒ(x) - A|＜ε
    </span>
    则称函数ƒ当x趋于x<sub>0</sub>时以A为极限，记作
    <span class="oneline">
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code> = A
    </span>
</p>
<p class="warn">
    温馨提示：单侧极限类似的。
</p>
<h2>
    四则运算法则
</h2>
<p>
    若极限<code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>与
    <code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code>
    都存在，则函数ƒ±g,ƒ·g当x→x<sub>0</sub>时极限也存在，且
    <span class="oneline">
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)±g(x)"]</code>=
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>±
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code>
    </span>
    <span class="oneline">
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)g(x)"]</code>=
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>·
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code>
    </span>
    又若 <code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code>≠0，则ƒ/g当x→x<sub>0</sub>时极限也存在，且有
    <span class="oneline">
        <code> ["limt",["join","x→",["rightBottom","x","0"]],["division","ƒ(x)","g(x)"]]</code>=
        <code>
            ["division",["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"], ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]]
        </code>
    </span>
</p>
<h2>
    重要性质
</h2>
<p>
    <span class="title">
        定理（唯一性）
    </span>
    若极限<code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>存在，则此极限是唯一的。
</p>
<p>
    <span class="title">
        定理（局部有界性）
    </span>
    若极限<code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>存在，则ƒ在x<sub>0</sub>在某领域U<sup>o</sup>(x<sub>0</sub>;δ<sup>'</sup>)内有界。
</p>
<p>
    <span class="title">
        定理（保不等式性）
    </span>
    设<code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>与<code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code>都存在，
    且在某领域U<sup>o</sup>(x<sub>0</sub>;δ<sup>'</sup>)内有ƒ(x)≤g(x)，则
    <span class="oneline">
        <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>≤<code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code>
    </span>
</p>
<p>
    <span class="title">
        定理（迫敛性）
    </span>
    设
    <code> ["limt",["join","x→",["rightBottom","x","0"]],"ƒ(x)"]</code>=<code> ["limt",["join","x→",["rightBottom","x","0"]],"g(x)"]</code></span>=
    A，且在某领域U<sup>o</sup>(x<sub>0</sub>;δ<sup>'</sup>)内有
    <span class="oneline">
        ƒ(x) ≤ h(x) ≤ g(x)
    </span>
    则<code> ["limt",["join","x→",["rightBottom","x","0"]],"h(x)"]</code>= A
</p>